Magnetoelastic coupling and long-range magnetic ordering in two-dimensional ferromagnets

Normal modes and possibility of spatially inhomogeneous phases for a 2D ferromagnet with biquadratic and magnetoelastic interactions

“…However, the account of the magnetodipolar interaction leads to the stabilization of the longrange magnetic order in 2D-systems [17]. The same effect has also the influence of the magnetoelastic interaction [18][19][20]. However, these mechanisms of the long-range magnetic order stabilization are different.…”

Long‐range order in two‐dimensional ferromagnets: Magnetoelastic effects

“…[8]. It is evident that (i) dynamic interaction makes a contribution only when in-plane phase is realized and in perpendicular phase it is equal to zero; (ii) its contribution is proportional to .…”

“…Generally speaking, one should take into account dynamic interactions between magnons and phonons by quantizing the tensor of deformations u ij = (0) ij u + (1) ij u , where the first quantity concerns spontaneous deformations and the second describes creation and annihilation of phonons [8], (1) ,…”

“…It was shown that magnetoelastic coupling may stabilize magnetic order in antiferromagnets [7]. Later this statement was proved for S = 1 Heisenberg ferromagnet and XY model [8]. The influence of magnetoelastic coupling and dipolar interaction on long-range order in ferromagnets has also been studied [9].…”

Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

“…According to the Mermin-Wagner theorem, there is no long-range magnetic order in 2D isotropic systems at any nonzero temperature [1]. However the account of the long-range relativistic interactions such as magnetic dipole interaction or/and magnetoelastic interaction breaks the symmetry of the system and, consequently, leads to the realization of a long-range magnetic order [2][3][4].…”